System and method for determining confidence measurements of single volume elements in computer tomography

ABSTRACT

A method for determining confidence values for volume units includes acquiring real projections of an object in a tomography system, reconstructing an image of the object from the real projections, generating artificial projections, for each volume unit comparing the real projections with the artificial projections and generating a confidence measure for each of the volume units.

BACKGROUND OF THE INVENTION

The subject matter disclosed herein relates to computer tomography, andmore particularly to determining quality of individual voxels involumetric models.

Tomography refers to imaging by sections or sectioning, through the useof any kind of penetrating wave, such as x-rays. A device used intomography is called a tomograph, while the image produced is atomogram. There are two basic steps in tomography: 1) acquisition ofx-ray projections of an object; and 2) reconstruction of the capturedx-ray projections to create a volumetric representation of the object,in which the volume is constructed of “voxels”. A voxel (volumetricpixel or, more correctly, Volumetric Picture Element) is a volumeelement, representing a value on a regular grid in three-dimensionalspace. This is analogous to a pixel, which represents 2D image data in abitmap (which is sometimes referred to as a pixmap).

During the acquisition phase, x-rays are emitted by an x-ray source froma focal spot, some of which penetrate the object. X-rays that penetratethe object are partially absorbed by the object. A detector records thex-rays and generates x-ray projections as digital images. The x-rayprojections are usually saved on a computer hard drive or more generallyin a computer memory. A detector can include a two dimensional array ora one dimensional array of pixels. Usually, to create a set of x-rayprojections, the object is rotated at discrete intervals over 360° usingthe manipulation system, and at every rotational position one x-rayprojection is generated. It is also possible to rotate the object overless than 360° or to rotate the object continuously.

During the reconstruction phase, the recorded x-ray projections are usedto calculate the volume. Commonly used methods for reconstructioninclude but are not limited to: filtered backprojection,Feldkamp-Davis-Kress (FDK) iterative techniques (e.g., algebraicreconstruction technique (ART), simultaneous algebraic reconstructiontechnique (SART), and statistical methods (e.g., maximum-likelihoodexpectation-maximization (ML-EM)).

As described above, voxels are comparable to pixels but have x-y-zcoordinates instead of x-y coordinates. In addition, each voxeldescribes the x-ray absorption coefficient at corresponding objectposition. Currently there is no suitable method for determining thequality of a voxel or how well a voxel is reconstructed (i.e., voxelconfidence). There can be situations where artifacts can't bedistinguished from real failures and details in the reconstructedvolume. This leads to misinterpretation and detection problems withautomated analysis algorithms.

BRIEF DESCRIPTION OF THE INVENTION

According to one aspect of the invention, a method for determiningconfidence values for volume units is described. The method includesacquiring real projections of an object in a tomography system,reconstructing an image of the object from the real projections,generating artificial projections, for each volume unit comparing thereal projections with the artificial projections and generating aconfidence measure for each of the volume units.

According to another aspect of the invention, a computer program productfor method for determining confidence values for volume units isdescribed. The computer program product includes a non-transitorycomputer readable medium storing instructions for causing a computer toimplement a method. The method includes acquiring real projections of anobject in a tomography system, reconstructing an image of the objectfrom the real projections, generating artificial projections, for eachvolume unit comparing the real projections with the artificialprojections and generating a confidence measure for each of the volumeunits.

According to yet another aspect of the invention, a system fordetermining confidence values for volume units is described. The systemincludes a source, an object configured to receive waves from the wavesource, an image detector configured to record attenuated waves thatgenerate real projections from the object, a computing system coupled tothe wave source and the image detector, a wave controller coupled to thewave source and to the computing system, a manipulation controllercoupled to the object and to the computing system, a data acquisitionmodule coupled to the image detector and to the computing system and aprocess residing on the computing system configured to acquire the realprojections from the image detector, reconstruct an image of the objectfrom the real projections, generate artificial projections, for eachvolume unit compare the real projections with the artificial projectionsand generate a confidence measure for each of the volume units.

These and other advantages and features will become more apparent fromthe following description taken in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWING

The subject matter, which is regarded as the invention, is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 illustrates a system for determining confidence measurements ofsingle volume elements in computed tomography;

FIG. 2 illustrates an example of a volume that can be acquired by thesystem of FIG. 1.

FIG. 3 illustrates an individual volume slice;

FIG. 4 illustrates a probability distribution plot for “good” and “bad”voxels;

FIG. 5 illustrates a flow chart for a method of determining confidencemeasurements in accordance with exemplary embodiments;

FIG. 6 illustrates an individual volume slice;

FIG. 7 illustrates an example of a probability distribution plot for“good” and “bad” voxels according to the selected material;

FIG. 8 illustrates an example of a probability distribution plot forvoxels with low confidence values;

FIG. 9 illustrates and example of an intersection table;

FIG. 10 illustrates an example of a probability distribution plot for“good” and “bad” voxels;

FIG. 11 illustrates an example of an intersection table;

FIG. 12 illustrates an example of a probability distribution plot inwhich the probability distributions for both the materials m₂, m₁ arerelatively close to one another;

FIG. 13 illustrates a flow chart for a method of determining confidencemeasurements in accordance with exemplary embodiments; and

FIG. 14 illustrates an exemplary embodiment of a computing system thatcan be used in determining confidence measurements of single volumeelements in computed tomography.

The detailed description explains embodiments of the invention, togetherwith advantages and features, by way of example with reference to thedrawings.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates a system 100 for determining confidence measurementsof single volume elements in computed tomography. For illustrativepurposes x-ray waves are discussed in exemplary embodiments. It will beappreciated that any other penetrating wave such as but not limited tomicrowaves, sound waves, x-rays, eddy current and electromagnetic wavesare contemplated in other exemplary embodiments. The system 100 includesan x-ray source 105 having a focal spot 106 from which x-ray beams 107are emitted. The x-ray source 105 is controlled by an x-ray controller110. The system 100 further includes an object 115 through which thex-ray beams 107 pass, and from which attenuated x-ray beams 108 pass.The object 115 is coupled to a manipulation controller 120 that rotatesthe object 115 through several positions in an x-y-z coordinate system101. The system 100 further includes an x-ray detector 125 onto whichprojections 116 of the object 115 are displayed. The attenuated x-raybeams 108 generate individual pixels 117 on the detector 125. Theindividual pixels 117 represent attenuated values from the attenuatedx-ray beams 108 as further described herein. The system 100 furtherincludes a data acquisition module 130 for collecting the acquired data(e.g., pixel 117 data) from the detector 125. A computing system 135 iscoupled to the x-ray controller 110 to control the generation of thex-ray beams 107. The computing system 135 is also coupled to themanipulation controller 120 to control the rotation of the object 115.The computing system 135 is further coupled to the data acquisitionmodule 130 for acquiring, storing and manipulating the acquired data asfurther described herein.

FIG. 2 illustrates an example of a volume 200 that can be acquired bythe system 100 of FIG. 1. The volume 200 represents a reconstructedimage of an object (e.g., the object 115) that can be generated fromvarious techniques described herein. The object 115 is illustratedgenerically as a cylinder. It will be appreciated that the object 115can be any object to be evaluated. In the example, the volume 200includes four volume slices 205, 210, 215, 220. Each of the volumeslices 205, 210, 215, 220 includes voxels, such as a voxel 225. As such,each of the volume slices 205, 210, 215, 220 includes sixteen voxels,and the volume 200 has sixty four voxels. It will be appreciated thatthe example of FIG. 2 is a simplified example and that reconstructedimage can include varying voxel numbers.

The system 100 provides quantitative information about thereconstruction quality/error of single volume elements without takingfurther external information into account. In exemplary embodiments, thesystem 100 can automatically define the confidence interval.Alternatively, the user can define the confidence interval. The system100 can implement several methods to determine the quality of eachvolume element (i.e., voxel) of the reconstructed data set. A voxelconfidence map is then generated from the internal process data of thereconstruction.

The methods described herein are not tied to a specific technique forcalculating the representation (e.g., ART, SART, ML-EM and FDK). Assuch, different techniques can be compared on a uniform basis whenconsidering voxel confidence. Furthermore, the probability distributionaffords stochastic methods to fuse representations of several techniquesto the resulting representation.

The methods described herein measure the confidence of the reconstructedvoxel density by the projection data. In exemplary embodiments,measurement of the confidence of the reconstructed voxel density by theprojected data can be attained by calculating the deviation between realprojection data and artificial projection data. As such, as furtherdescribed herein, as real projections (i.e., real pixel values) areacquired, forward projection is implemented to also calculate artificialpixel values for corresponding to each acquired pixel value. FIG. 3illustrates an individual volume slice 300 (e.g., one of volume slices205, 210, 215, 220 of FIG. 2). The volume slice includes several objects305, 310, 315, 320 each made up from voxels such as a voxel 325 (v_(j)).Each voxel, including the voxel 325 is calculated from real pixel valuesfrom several passes of x-ray beams, represented by ray_(i). Computationof error, that is a deviation between each real pixel value and asummation of artificial pixel values from forward projection, isperformed. For every pixel in the projection images, an error measure,f_(i), is computed:

$\begin{matrix}{f_{i} = {p_{i} - {\sum\limits_{n}{w_{in}v_{n}}}}} & (1)\end{matrix}$

Here, p_(i) is the pixel value in the projection data, v_(n) is thevoxel density in the volumetric data, and w_(in) is a weighting factor.The weighting factor is a value selected that determines the influence aparticular voxel in the voxel density v_(n) on the particular ith ray,ray_(i), that passes through the voxel. The sum over all n forw_(in)v_(n) is an artificial pixel value, calculated from all voxels inthe voxel density v_(n) through which the each ray_(i) passed. In thisway forward projection is implemented to generate the artificial pixeldata. As described herein, for every real pixel value acquired, thedeviation is calculated based on the artificial pixel value computedwith forward projection. A histogram of the error measure values f, iscomputed for the voxel v_(j), and the histogram is converted to aprobability distribution, which determines the confidence value of thevoxel, v_(j). FIG. 4 illustrates a probability distribution plot 400 ofprobability density, P(f_(i)) versus error measure, f_(i), for “good”and “bad” voxels. A voxel can be determined to be “good” if thecorrespondent probability distribution of f_(i) falls within aconfidence interval 405. As such, the probability distributionrepresents the confidence measure. If a significant part of theprobability distribution falls in other intervals 410, 415 thecorrespondent voxel can be considered as “bad”. This is illustrated inthe plot 401. The confidence interval can be selected prior to thedistribution. It will be appreciated that the selection of “good” and“bad” voxels tells the user a measure of quality of the resultingvolumetric representation. As can be appreciated in FIG. 4, highconfidence values include a distribution that is tall relative to thewidth, and the lower confidence values are relatively shorter and wider.It will be appreciated that predetermined values can be selected by auser or automatically by the system 100.

FIG. 5 illustrates a flow chart for a method 500 of determiningconfidence measurements in accordance with exemplary embodiments. Atblock 505, the system 100 acquires real projections. Many onedimensional or two dimensional x-ray images are taken via the detector125. As described herein, the real projections include many pixels. Eachpixel represents a value that corresponds to the attenuation of thecorresponding x-ray beams 107, that are emitted from the focal spot 106and hits that pixel on the detector 125. Once all projections areacquired, at block 510, the system 100 reconstructs the volume slices ofthe object 115 from the x-ray projections. Reconstruction is amathematical computing method that generates volume slices from x-rayimages. Several examples of reconstruction algorithms have beendescribed herein including, but not limited to: filtered backprojection,FDK, iterative techniques such as ART and SART and statistical methodssuch as ML-EM. It will be appreciated that any reconstruction algorithmcan be implemented. At least one of more slices represents a volumetricimage of a real object. As described herein, each slice includes anumber of voxels that each represents an attenuation coefficient at thecorresponding position in the real object 115. At block 520, the system100 generates artificial projections via forward projection. Forwardprojection thus generates artificial projection data from volume slicesusing the geometric projection models of the system 100. The artificialprojections can be one dimensional or two dimensional artificiallycomputed images that include several pixels. At block 525, the system100 performs an evaluation for every voxel v_(j), by comparing the realprojections acquired at block 505 with the artificial projectionscomputed at block 520. The system 100 further computes the histogramsand probabilities in the confidence intervals (see FIG. 4) as aconfidence measure for each voxel v_(j). It will be appreciated that thesystem 100 stores each of the acquired real projections, the artificialprojections, and the confidence data (e.g., probability distributions).At block 530, the system 100 determines the confidence levels from theprobability distributions. Each voxel is assigned a confidence measure.The entity of confidence measures over all voxels results in confidencemeasure distribution for all volume slices. The confidence measure canalso be saved in the system 100 and displayed for a user as furtherdescribed herein.

In exemplary embodiments, the reconstructed voxel density can also bevaried and exchanged with a predefined density value (e.g., material andair, alternatingly). The method can also be easily extended for usagewith more than just two predefined densities (e.g. air, material1,material2 and the like). The systems and methods described hereinmeasure the support of each of the predefined densities by theprojection data based on calculation of the histogram and probabilitycalculation in the confidence interval 405. The measure for the supportcan be expressed as the probability for material (Pm) and air (Pa). Asdescribed further herein, the systems and methods described hereinimplement probabilistic evidence theory (e.g., Dempster-Shafer-Theory).The probabilistic theory is also used to measure and to considerconflicts for the support of different predefined density values (e.g.,if both material and air have the same support in the projection data,the conflict is high and thus, the confidence for this voxel is low).FIG. 6 illustrates an individual volume slice 600 (e.g., one of volumeslices 205, 210, 215, 220 of FIG. 2). The volume slice includes severalobjects 605, 610, 615, 620 each made up from voxels such as a voxel 625(v_(j)). Each voxel, including the voxel 625 includes real pixel valuesfrom several passes of x-ray beams, represented by ray_(i). Computationof error, that is a deviation between each real pixel value and asummation of artificial pixel values from forward projection, isperformed. For every pixel in the projection images, an error measure:

$\begin{matrix}\left. {f_{i} = {p_{i} - {\sum\limits_{n}{w_{in}v_{n}}} + {w_{ij}\left( {v_{j} - m_{x}} \right)}}} \right) & (2)\end{matrix}$

is computed. Here, p, is the pixel value in the projection data, is thevoxel density in the volumetric data, and w_(in) is a weighting factor.The weighting factor is a value selected that determines the influenceof a particular voxel in the voxel density v_(n) n the particular ray,that passes through the voxel. The sum over all n for w_(in)v_(n) is anartificial pixel value, calculated from all voxels in the voxel densityv_(n) through which the each ray, passed. In exemplary embodiments, anadditional artificial value, w_(ij)(v_(j)−m_(x)) is added to thesummation. The voxel v_(j) is adjusted by the density value of thevoxels through which the individual x-ray beams, ray_(i), pass. Forexample, x may have two values, x=1 for air and x=2 for the material ofthe object 115 under test. In exemplary embodiments, a histogram can beconstructed from equation (2) for the m₁ values for the voxel v_(j). Thehistogram can then be converted to a probability distribution. The samesteps are repeated for m₂, that is, first a histogram is constructedfrom equation (2) for the m₂ values for the voxel v_(j), and can then beconverted to a probability distribution. A confidence measure can thenbe calculated for each of m₁ and m₂ to attain values P(0|m₁) andP(0|m₂), respectively. These values can be understood as probabilitythat the material m₁ and m₂ are the right ones. FIG. 7 illustrates aprobability distribution plot 700 for a voxel according to thesubstituted materials m₁ and m₂. The probability distribution iscalculated from histograms like in FIG. 4. In exemplary embodiments, avoxel can be “good” when one of the probability for one of the materialsis higher relative to the other probability for the other material. Inthe example in FIG. 7, the probability 705 for the material m₂ has abetter confidence value than the probability 710 for the material m₁. Assuch, the user or the system 100 can select that material associatedwith the probability 705 is more probable than the material associatedwith probability 710. This voxel can also be considered as a “good”voxel. FIG. 8 illustrates another probability distribution plot 800 forvoxels with low confidence values. In the example in FIG. 8, theprobabilities 805, 810 for both the materials m₂, m₁ are relativelyclose to one another. This example would be considered a conflictsituation where both materials are supported equally by the projections.This voxel can also be considered as a “bad” voxel. It will beappreciated that the user can select predetermined spread values betweenthe probability distributions to determine whether a voxel is “good” or“bad” and whether there is a conflict situation.

In exemplary embodiments, evidence theory (e.g., Dempster-Shafer theory)can determine whether the voxels are “good” or “bad”. For the results ofthe probability distribution in FIG. 7, for the material m₂, theprobability of the union of m₂ and m₁ can be computed, that is, theprobability of P(m₂∪m₁=1−P(0|m₂)=0,1). Similarly, for the material m₁,the probability of the union of m₂ and m₁ can be computed, that is, theprobability of P(m₂∪m₁=1−P(0|m₁)=0,7). For both materials anintersection table can be constructed. FIG. 9 illustrates anintersection table 900 illustrating the intersections for theprobability distributions from both Dempster-Shafer theory and evidencetheory. FIG. 10 illustrates a probability distribution plot 1000 for“good” and “bad” voxels according to the selected material, with theprobability distributions P_(F) extracted from the intersection table.The distribution plot provides further evidence that the voxel relatedto the material m₂ is a “good” voxel.

For the results of the probability distribution in FIG. 8, for thematerial m₂, the probability of the union of m₂ and m₁ can be computed,that is, the probability of P(m₂∪m₁)=1−P(0|m₂)=0,1. Similarly, for thematerial m₁, the probability of the union of m₂ and m₁ can be computed,that is, the probability of P(m₂∪m₁)=1−P(0|m₁)=0,2. For both materialsan intersection table can be constructed. FIG. 11 illustrates anintersection table 1100 illustrating the intersections for theprobability distributions from both Dempster-Shafer theory and evidencetheory. FIG. 12 illustrates a probability distribution plot 1200 inwhich the probability distributions for both the materials m₂, m₁ arerelatively close to one another, and with the probability distributionsP_(F) extracted from the intersection table. The distribution plotprovides further evidence that this example would be considered aconflict situation.

FIG. 13 illustrates a flow chart for a method 1300 of determiningconfidence measurements in accordance with exemplary embodiments. Atblock 1305, the system 100 acquires real projections. Many onedimensional or two dimensional x-ray images are taken via the detector125. As described herein, the real projections include many pixels. Eachpixel represents a value that corresponds to the attenuation of thecorresponding x-ray beams 107, that are emitted from the focal spot 106and hits that pixel on the detector 125. Once all projections areacquired, at block 1310, the system 100 reconstructs the image of theobject 115 from the x-ray images. Reconstruction is the mathematicalcomputing method that generates volume slices from x-ray images. Severalexamples of reconstruction algorithms have been described hereinincluding, but not limited to: filtered backprojection, FDK, iterativetechniques such as ART and SART and statistical methods such as ML-EM.It will be appreciated that any reconstruction algorithm can beimplemented. At least one of more slices represents a volumetric imageof a real object. As described herein, each slice includes a number ofvoxels that each represents an attenuation coefficient at thecorresponding position in the real object 115. At block 1320, theindividual voxels can be manipulated such as described above withrespect to material density values. In exemplary embodiments, everysingle voxel can be set to a predefined specific value. The predefinedspecific value can be a material density value gained from aprioriknowledge as described herein. To compute confidence measuredistribution for a given volume it may be necessary to repeat this stepmany times as described above. At least one of more slices represents avolumetric image of a real object but with manipulated voxels. Thechanged volume slices are used in the calculation for the probabilitydistributions as described herein, but are not necessarily used in thereconstruction of the projections 116. At block 1330, the system 100generates artificial projections via forward projection. Forwardprojection thus generates artificial projection data from volume slicesusing the geometric projection models of the system 100. The artificialprojections can be one dimensional or two dimensional artificiallycomputed images that include several pixels. At block 1335, the system100 performs an evaluation for every voxel v_(j), by comparing the realprojections acquired at block 1305 with the artificial projectionscomputed at block 1330. The system 100 further computes the histogramsand probabilities in the confidence intervals as a confidence measurefor each voxel v_(j). The system 100 further applies the Dempster-Shaferand evidence theories and from the computation of the Dempster-Shaferand evidence theories, computes the confidence measure of the voxels(see FIGS. 7-12). It will be appreciated that the system 100 stores eachof the acquired real projections, the artificial projections, and theconfidence data (e.g., probability distributions). The system 100 canperform the voxel manipulations at block 1320 and forward projection atblock 1330 multiple times depending on the number and types of materialsunder evaluation. As such, at block 1336, the system 100 determines ifthere is an additional material to consider. If there is an additionalmaterial to consider at block 1336, then the system repeats the method1300 beginning at block 1320. At block 1340, the system 100 determinesthe confidence levels from the probability distributions. Each voxel isassigned a confidence measure. The entity of confidence measures overall voxels results in confidence measure distribution for all volumeslices. The confidence measure can also be saved in the system 100 anddisplayed for a user as further described herein.

The computing system 135 of FIG. 1 can be any suitable computing deviceas now described. FIG. 14 illustrates an exemplary embodiment of acomputing system 1400 that can be used in determining confidencemeasurements of single volume elements in computed tomography. Themethods described herein can be implemented in software (e.g.,firmware), hardware, or a combination thereof. In exemplary embodiments,the methods described herein are implemented in software, as anexecutable program, and is executed by a special or general-purposedigital computer, such as a personal computer, workstation,minicomputer, or mainframe computer. The system 1400 therefore includesgeneral-purpose computer 1401.

In exemplary embodiments, in terms of hardware architecture, as shown inFIG. 14, the computer 1401 includes a processor 1405, memory 1410coupled to a memory controller 1415, and one or more input and/or output(I/O) devices 1440, 1445 (or peripherals) that are communicativelycoupled via a local input/output controller 1435. The input/outputcontroller 1435 can be, but is not limited to, one or more buses orother wired or wireless connections, as is known in the art. Theinput/output controller 1435 may have additional elements, which areomitted for simplicity, such as controllers, buffers (caches), drivers,repeaters, and receivers, to enable communications. Further, the localinterface may include address, control, and/or data connections toenable appropriate communications among the aforementioned components.

The processor 1405 is a hardware device for executing software,particularly that stored in memory 1410. The processor 1405 can be anycustom made or commercially available processor, a central processingunit (CPU), an auxiliary processor among several processors associatedwith the computer 1401, a semiconductor based microprocessor (in theform of a microchip or chip set), a macroprocessor, or generally anydevice for executing software instructions.

The memory 1410 can include any one or combination of volatile memoryelements (e.g., random access memory (RAM, such as DRAM, SRAM, SDRAM,etc.)) and nonvolatile memory elements (e.g., ROM, erasable programmableread only memory (EPROM), electronically erasable programmable read onlymemory (EEPROM), programmable read only memory (PROM), tape, compactdisc read only memory (CD-ROM), disk, diskette, cartridge, cassette orthe like, etc.). Moreover, the memory 1410 may incorporate electronic,magnetic, optical, and/or other types of storage media. Note that thememory 1410 can have a distributed architecture, where variouscomponents are situated remote from one another, but can be accessed bythe processor 1405.

The software in memory 1410 may include one or more separate programs,each of which comprises an ordered listing of executable instructionsfor implementing logical functions. In the example of FIG. 14, thesoftware in the memory 1410 includes the confidence measurement methodsdescribed herein in accordance with exemplary embodiments and a suitableoperating system (OS) 1411. The OS 1411 essentially controls theexecution of other computer programs, such the confidence measurementsystems and methods as described herein, and provides scheduling,input-output control, file and data management, memory management, andcommunication control and related services.

The confidence measurement methods described herein may be in the formof a source program, executable program (object code), script, or anyother entity comprising a set of instructions to be performed. When asource program, then the program needs to be translated via a compiler,assembler, interpreter, or the like, which may or may not be includedwithin the memory 1410, so as to operate properly in connection with theOS 1411. Furthermore, the confidence measurement methods can be writtenas an object oriented programming language, which has classes of dataand methods, or a procedure programming language, which has routines,subroutines, and/or functions.

In exemplary embodiments, a conventional keyboard 1450 and mouse 1455can be coupled to the input/output controller 1435. Other output devicessuch as the I/O devices 1440, 1445 may include input devices, forexample but not limited to a printer, a scanner, microphone, and thelike. Finally, the I/O devices 1440, 1445 may further include devicesthat communicate both inputs and outputs, for instance but not limitedto, a network interface card (NIC) or modulator/demodulator (foraccessing other files, devices, systems, or a network), a radiofrequency (RF) or other transceiver, a telephonic interface, a bridge, arouter, and the like. The I/O devices 1440, 1445 further include thex-ray controller 110, the manipulation controller 120 and the dataacquisition module 130 of FIG. 1. The system 1400 can further include adisplay controller 1425 coupled to a display 1430. In exemplaryembodiments, the system 1400 can further include a network interface1460 for coupling to a network 1465. The network 1465 can be an IP-basednetwork for communication between the computer 1401 and any externalserver, client and the like via a broadband connection. The network 1465transmits and receives data between the computer 1401 and externalsystems. In exemplary embodiments, network 1465 can be a managed IPnetwork administered by a service provider. The network 1465 may beimplemented in a wireless fashion, e.g., using wireless protocols andtechnologies, such as WiFi, WiMax, etc. The network 1465 can also be apacket-switched network such as a local area network, wide area network,metropolitan area network, Internet network, or other similar type ofnetwork environment. The network 1465 may be a fixed wireless network, awireless local area network (LAN), a wireless wide area network (WAN) apersonal area network (PAN), a virtual private network (VPN), intranetor other suitable network system and includes equipment for receivingand transmitting signals.

If the computer 1401 is a PC, workstation, intelligent device or thelike, the software in the memory 1410 may further include a basic inputoutput system (BIOS) (omitted for simplicity). The BIOS is a set ofessential software routines that initialize and test hardware atstartup, start the OS 1411, and support the transfer of data among thehardware devices. The BIOS is stored in ROM so that the BIOS can beexecuted when the computer 1401 is activated.

When the computer 1401 is in operation, the processor 1405 is configuredto execute software stored within the memory 1410, to communicate datato and from the memory 1410, and to generally control operations of thecomputer 1401 pursuant to the software. The confidence measurementmethods described herein and the OS 1411, in whole or in part, buttypically the latter, are read by the processor 1405, perhaps bufferedwithin the processor 1405, and then executed.

When the systems and methods described herein are implemented insoftware, as is shown in FIG. 14, the methods can be stored on anycomputer readable medium, such as storage 1420, for use by or inconnection with any computer related system or method.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

In exemplary embodiments, where the confidence measurement methods areimplemented in hardware, the confidence measurement methods describedherein can implemented with any or a combination of the followingtechnologies, which are each well known in the art: a discrete logiccircuit(s) having logic gates for implementing logic functions upon datasignals, an application specific integrated circuit (ASIC) havingappropriate combinational logic gates, a programmable gate array(s)(PGA), a field programmable gate array (FPGA), etc.

Technical effects include but are not limited to providing a display ofconfidence level with indicators such as color coding. The systems andmethods described herein also provide a user with a confidence levelindicating the quality of a voxel in an acquired image. Utilization ofthe confidence information increases the reconstruction quality withinan iterative reconstruction algorithm.

While the invention has been described in detail in connection with onlya limited number of embodiments, it should be readily understood thatthe invention is not limited to such disclosed embodiments. Rather, theinvention can be modified to incorporate any number of variations,alterations, substitutions or equivalent arrangements not heretoforedescribed, but which are commensurate with the spirit and scope of theinvention. Additionally, while various embodiments of the invention havebeen described, it is to be understood that aspects of the invention mayinclude only some of the described embodiments. Accordingly, theinvention is not to be seen as limited by the foregoing description, butis only limited by the scope of the appended claims.

1. A method for determining confidence values for volume units, themethod comprising acquiring real projections of an object in atomography system; reconstructing an image of the object from the realprojections; generating artificial projections; for each volume unit:comparing the real projections with the artificial projections; andgenerating a confidence measure for each of the volume units.
 2. Themethod as claimed in claim 1 wherein the volume units are voxels.
 3. Themethod as claimed in claim 2 wherein the object is represented by volumeslices.
 4. The method as claimed in claim 3 wherein reconstructing theimage of the object from the real projections comprises generating thevolume slices from the real projections.
 5. The method as claimed inclaim 1 wherein each real projection includes a pixel value.
 6. Themethod as claimed in claim 5 further comprising computing an errormeasure value for each pixel value.
 7. The method as claimed in claim 6wherein the error measure value is a difference between the pixel value,and a summation of a product of a weighting factor and a first voxelvalue.
 8. The method as claimed in claim 6 wherein the error measurevalue is a difference between the pixel value, and a sum a product of aweighting factor and a first voxel value, wherein product is manipulatedby exchanging of the voxel value with a first artificial value.
 9. Themethod as claimed in claim 8 wherein the artificial material pixel valueis a product of a material weighting factor and a difference of a secondvoxel value and a material density value.
 10. The method as claimed inclaim 7 wherein the generating of the confidence measure for a voxelcomprises computing at least one error measure.
 11. The method asclaimed in claim 10 further comprising computing a manifold of errormeasures for different rays through a voxel and building of a histogramfrom the manifold of error measures.
 12. The method as claimed in claim11 further comprising: converting the histogram to a probabilitydistribution: and deriving a characteristic value from this probabilitydistribution.
 13. The method as claimed in claim 12 wherein thecharacteristic value is derived through an integration of theprobability distribution within an interval.
 14. The method as claimedin claim 13 wherein the confidence measure is derived from thecharacteristic value.
 15. The method as claimed in claim 8 wherein priorto the computation of at least one error measure, a voxel value ismanipulated by exchanging of the voxel value with at least oneartificial value.
 16. The method as claimed in claim 13 wherein thecharacteristic value is a first characteristic value that corresponds tothe first artificial value.
 17. The method as claimed in claim 13wherein the characteristic value is at least one of a second value andany further characteristic values that correspond to at least one of thesecond value and any further artificial value.
 18. The method as claimedin claim 1 wherein the confidence measure is derived from at least oneof a first characteristic value, a second characteristic value and anyfurther characteristic values from evidence theory.
 19. A computerprogram product for method for determining confidence values for volumeunits, the computer program product including a non-transitory computerreadable medium storing instructions for causing a computer to implementa method, the method comprising: acquiring real projections of an objectin a tomography system; reconstructing an image of the object from thereal projections; generating artificial projections; for each volumeunit: comparing the real projections with the artificial projections;and generating a confidence measure for each of the volume units.
 20. Asystem for determining confidence values for volume units, the systemcomprising: a source; an object configured to receive waves from thewave source; an image detector configured to record attenuated wavesthat generate real projections from the object; a computing systemcoupled to the wave source and the image detector; a wave controllercoupled to the wave source and to the computing system; a manipulationcontroller coupled to the object and to the computing system; a dataacquisition module coupled to the image detector and to the computingsystem; and a process residing on the computing system configured to:acquire the real projections from the image detector; reconstruct animage of the object from the real projections; generate artificialprojections; for each volume unit: compare the real projections with theartificial projections; and generate a confidence measure for each ofthe volume units.